Gun control advocates argue that the proposal would effectively loosen gun control laws in tightly restricted locations such as New York City.

The bill also contained measures requiring the Department of Justice to produce to Congress a report about bump stock modifications and another that tightens National Instant Criminal Background Check System reporting requirements in the wake of last month's church shooting in Texas, perpetrated by a gunman whose prior domestic violence conviction was not reported to the system.

In the Senate, the Concealed Carry Reciprocity Act will need to clear a 60-vote threshold to pass.